Question
Solve the equation(The real numbers system)
x∈/R
Alternative Form
No real solution
Evaluate
3×2x2−2x=2(3x−6)
Multiply the numbers
6x2−2x=2(3x−6)
Expand the expression
More Steps

Evaluate
2(3x−6)
Apply the distributive property
2×3x−2×6
Multiply the numbers
6x−2×6
Multiply the numbers
6x−12
6x2−2x=6x−12
Move the expression to the left side
6x2−8x+12=0
Substitute a=6,b=−8 and c=12 into the quadratic formula x=2a−b±b2−4ac
x=2×68±(−8)2−4×6×12
Simplify the expression
x=128±(−8)2−4×6×12
Simplify the expression
More Steps

Evaluate
(−8)2−4×6×12
Multiply the terms
More Steps

Multiply the terms
4×6×12
Multiply the terms
24×12
Multiply the numbers
288
(−8)2−288
Rewrite the expression
82−288
Evaluate the power
64−288
Subtract the numbers
−224
x=128±−224
Solution
x∈/R
Alternative Form
No real solution
Show Solution

Solve the equation(The complex numbers system)
Solve using the quadratic formula in the complex numbers system
Solve by completing the square in the complex numbers system
Solve using the PQ formula in the complex numbers system
x1=32−314i,x2=32+314i
Alternative Form
x1≈0.6˙−1.247219i,x2≈0.6˙+1.247219i
Evaluate
3×2x2−2x=2(3x−6)
Multiply the numbers
6x2−2x=2(3x−6)
Expand the expression
More Steps

Evaluate
2(3x−6)
Apply the distributive property
2×3x−2×6
Multiply the numbers
6x−2×6
Multiply the numbers
6x−12
6x2−2x=6x−12
Move the expression to the left side
6x2−8x+12=0
Substitute a=6,b=−8 and c=12 into the quadratic formula x=2a−b±b2−4ac
x=2×68±(−8)2−4×6×12
Simplify the expression
x=128±(−8)2−4×6×12
Simplify the expression
More Steps

Evaluate
(−8)2−4×6×12
Multiply the terms
More Steps

Multiply the terms
4×6×12
Multiply the terms
24×12
Multiply the numbers
288
(−8)2−288
Rewrite the expression
82−288
Evaluate the power
64−288
Subtract the numbers
−224
x=128±−224
Simplify the radical expression
More Steps

Evaluate
−224
Evaluate the power
224×−1
Evaluate the power
224×i
Evaluate the power
More Steps

Evaluate
224
Write the expression as a product where the root of one of the factors can be evaluated
16×14
Write the number in exponential form with the base of 4
42×14
The root of a product is equal to the product of the roots of each factor
42×14
Reduce the index of the radical and exponent with 2
414
414×i
x=128±414×i
Separate the equation into 2 possible cases
x=128+414×ix=128−414×i
Simplify the expression
More Steps

Evaluate
x=128+414×i
Divide the terms
More Steps

Evaluate
128+414×i
Rewrite the expression
124(2+14×i)
Cancel out the common factor 4
32+14×i
Simplify
32+314i
x=32+314i
x=32+314ix=128−414×i
Simplify the expression
More Steps

Evaluate
x=128−414×i
Divide the terms
More Steps

Evaluate
128−414×i
Rewrite the expression
124(2−14×i)
Cancel out the common factor 4
32−14×i
Simplify
32−314i
x=32−314i
x=32+314ix=32−314i
Solution
x1=32−314i,x2=32+314i
Alternative Form
x1≈0.6˙−1.247219i,x2≈0.6˙+1.247219i
Show Solution
